\documentclass[12pt, a4paper]{article}
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\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{physics}
\graphicspath{ {./} }
\usepackage{ctex}
\usepackage{makecell}

\newcommand{\bvec}[1]{\mathbf{#1}}
\newcommand{\formula}[1]{\text{式} \ref{#1} }

\begin{document}
	一篇很怪的笔记，可能不太符合主流说法。
	
		\begin{table}[h]
		\begin{center}
			\begin{tabular}{|c|c|c|}
				\hline	
				学科 & 状态方程 & 动力学方程  \\
				\hline
				经典力学 & 
				\makecell
				{
					$T = \sum_i \frac{m_i v_i^2}{2}$ \\ 
					$V = V(\bvec r_1, \bvec r_2, ..., t)$\\
					$E_{mech} = T+V$\\
					$\bvec F_i = - \pdv{V}{\bvec r_i}$ \\
					机械能
				}
				&
				\makecell
				{
					$m_i \dv{\bvec v_i}{t} = \bvec F_i$ \\
					$\dd \bvec r_i = \bvec v_i \dd t$ \\
					牛顿第二定律
				}
			\\
			\hline
			分析力学 &
			\makecell{$L=L(q_1, q_2, ..., q'_1, q'_2,...,t)$\\Lagrange量} & 
			\makecell{$\dv{}{t} \pdv{L}{q'_i} = \pdv{L}{q}$ \\ $\dd q_i = q'_i \dd t$ \\ Euler-Lagrange 方程}
			\\
			\hline
			热力学（相场法）&
			\makecell{$F=F(p,T,\eta, c_1, c_2, ...)$\\自由能} &
			\makecell{$\pdv{c_i}{t} = \div (M_i \grad \pdv{F}{c_i})$\\守恒量的C-H方程\\$\pdv{\eta}{t} = - L \pdv{F}{\eta}$\\非守恒量的G-L方程}
			\\
			\hline
			量子力学 &
			\makecell{$\ket{\Psi} = \ket{\Psi(t)}$\\系统的ket （“波函数”）} &
			\makecell{$i \hbar \pdv{\ket{\Psi}}{t} = \hat H \ket{\Psi}$ \\ 薛定谔方程}
			\\
			\hline
			\end{tabular}
		\end{center}
		\caption{状态方程与守恒量}
	\end{table}
	
\end{document}
